# Combinatorial Properties and Recognition of Unit Square Visibility Graphs

## TL;DR

This paper explores the combinatorial characteristics of unit square visibility graphs and examines the computational complexity of recognizing and representing these graphs within constrained areas.

## Contribution

It provides new insights into the properties of USV and USGV and analyzes the difficulty of recognition problems for these graph classes.

## Key findings

- Identified key combinatorial properties of USV and USGV.
- Proved hardness results for recognition problems.
- Analyzed constraints for representing these graphs in small areas.

## Abstract

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem.

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Source: https://tomesphere.com/paper/1706.05906